Thousands of Tunisians have rallied to protest against what they see as a push by the Islamist-led government for constitutional changes that would degrade women's status in one of the Arab world's most liberal nations.

The protest on Monday by 6,000 mostly Tunisian women is the latest twist in a row over the role of Islam in a constitution being drawn up by a new assembly.

Tunisia's ruling Ennahda Movement is under pressure from both hardline Salafi Muslims, who are calling for the introduction of Islamic law, and secular opposition parties.

Activists are unhappy with a stipulation in a draft of the constitution that considers women to be "complementary to men" and want a pioneering 1956 law that grant women full equality with men to remain in place.

The protesters marched across main routes in the capital Tunis to demand that the government, led since October by Islamist moderates Ennahda, turn its attention instead to basic issues such as unemployment and regional development.

They carried banners reading: "Rise up women for your rights to be enshrined in the constitution" and "Ghannouchi clear off, Tunisian women are strong", referring to Ennahda's leader, Rachid Ghannouchi.

Sami Layouni, 40, was one of the few men attending the protest. "We are here to support women and to say there are men who stand for women's rights," he said, carrying a placard reading: "A woman is no complement, she is everything."

"We are proud of Tunisian women … and we will not let Islamists turn our spring into a winter," Layouni added.

Carrying a placard that called for equal rights, 52-year-old Fouzia Belgaid said last year's revolt should not have led to such debate in Tunisian society. "Normally, more important issues ought to be tackled like unemployment, regional development," she said. "Ennahda seems bent on making steps backwards but we are here to say that Tunisian women will not accept that. I fear for the future of my daughters who may grow up in a totally different Tunisia."

Ennahda was banned under former president Zine al-Abidine Ben Ali. After the leader was toppled in mass protests that sparked the Arab spring last year, Ennahda won the most seats in elections to a constituent assembly in October and formed a government in coalition with two secular parties.

The party has promised not to impose strict Muslim rules and to respect women's rights. One of its members, Farida al-Obeidi, who chairs the assembly's human rights and public freedoms panel, said the wording of the draft did not represent a backwards step for Tunisian women.

The draft stipulates "sharing of roles and does not mean that women are worth less than men", she said.

Activists are concerned that once approved, the new rules would lead to future setbacks. "Major retreats usually begin with one step," said Ahlam Belhadj, who chairs the Democratic Women's Association. "If we stay silent today, we will open the door to everything else and end up surprised by even more serious decisions," she said.